STRONG CONSISTENCY UNDER GAUSS-MARKOV CONDITION

Let Y-i=x(i)' beta+e(i), 1 less than or equal to i less than or equal to n, be a linear model, <(beta)over cap>(n)=(<(beta)over cap>(n1), .. ., <(beta)over cap>(np)) be the LS estimate of beta-(beta(1), ..., bet a(p))'. Denote by u(n) the (1,1)-element of [GRAPHICS] Assume that Ee( i)=0 and {e(i)} obeys the Gauss-Markov condition Ee(i)e(j)=sigma(2) de lta(ij). It is shown that [GRAPHICS] is a sufficient condition for <(b eta)over cap>(n1) to be strongly consistent. This condition is accurat e in the sense that for any e(n) --> 0, the condition[GRAPHICS] ceases to be sufficient. Some remarks are made concerning the necessary and/ or sufficient condition for <(beta)over cap>(n1) to be strongly consis tent.